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SeMA Journal

, Volume 74, Issue 2, pp 115–132 | Cite as

Dudley metric and continuity of functional integrals

Article
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Abstract

We prove that the Dudley metric is complete on the space of Young measures and then we study the uniform continuity of functional \(u\mapsto \int _{\Omega }f(t,u(t)) dt\) on subsets of \({\mathcal {L}}^{1}(\Omega , \mathbb R^{s})\). The results are applied on Sobolev space \({\mathcal {W}}^{1,1}(\Omega , \mathbb R^{m})\hookrightarrow {\mathcal {L}}^{1}(\Omega , \mathbb R^{m+m\times d})\) .

Keywords

Young measures Dudley metric Uniform integrability 

Mathematics Subject Classification

Primary 28A20 Secondary 28A33 49J45 54D35 

Notes

Acknowledgments

The author thanks warmly to the anonymous reviewers for their careful reading of this text; the relevant comments have clearly improved this work in terms of clarity and rigor of exposure.

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Copyright information

© Sociedad Española de Matemática Aplicada 2016

Authors and Affiliations

  1. 1.Faculty of Mathematics“Al. I. Cuza” UniversityIaşiRomania

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